A Note on Approximate Controllability of Fractional Semilinear Integrodifferential Control Systems via Resolvent Operators

Abstract

This article primarily focuses on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators. Two alternative sets of necessary requirements have been studied. In the first set, we use theories from functional analysis, the compactness of an associated resolvent operator, for our discussion. The primary discussion is proved in the second set by employing Gronwall’s inequality, which prevents the need for compactness of the resolvent operator and the standard fixed point theorems. Then, we extend the discussions to the fractional Sobolev-type semilinear integrodifferential systems. Finally, some theoretical and practical examples are provided to illustrate the obtained theoretical results.

Keywords

• fractional integrodifferential system
• approximate controllability
• Schauder’s fixed point theorem
• resolvent operators
• Sobolev-type system